The Introduction of the Reserve Clause in Major League Baseball: Evidence of Its Impact on Select Player Salaries During the 1880S

The Introduction of the Reserve Clause in Major League Baseball: Evidence of its Impact on Select Player Salaries During the 1880s

Jennifer K. Ashcraft Burlington Northern-Santa Fe Railway Company Fort Worth, TX 76131 Oﬃce: (817) 352-4919 E-mail: [email protected]

Craig A. Depken, II∗ Department of Economics The Belk College of Business UNC Charlotte Charlotte, NC 28223 Oﬃce: (704) 687-7484 Fax: (704) 687-6442 E-mail: [email protected]

∗ Corresponding author. Helpful suggestions by seminar participants at West Virginia University, Clemson University, the University of Georgia, and Wake Forest University are acknowledged. The usual caveat applies. The Introduction of the Reserve Clause in Major League Baseball: Evidence of its Impact on Select Player Salaries During the 1880s

Abstract

This paper investigates the impact of baseball’s reserve clause as it evolved from a “gentleman’s agreement” to a formal contract stipulation. Using a unique data set describing the salaries of 29 Major League Baseball players during the 1880s, we test whether average salaries, remuneration to marginal product, and the premium paid to a player for changing teams were materially impacted when the reserve clause became binding in 1887. The empirical results suggest that average salaries in the sample fell by approximately 10% after the reserve clause, controlling for player attributes and the overall macroeconomy. We also ﬁnd that the premium for moving to a new team was cut in half after the binding reserve clause was implemented, supporting the invariance principle postulated by Rottenberg (1956).

JEL Classiﬁcations: J31, J42, L83

Keywords: Sports economics, monopsony, free agency, negotiation 1 Introduction

Prior to 1974 the professional baseball labor market was characterized by the “reserve clause,” which tied a player’s services to his current team indeﬁnitely, thereby transfer- ring monopsony power to baseball team owners. The reserve clause was a constant source of friction between players and team owners throughout its history. These frictions were somewhat mitigated by arbitration, introduced in 1974, and free agency, introduced in 1976, both of which essentially removed the reserve clause for all but the least experienced players in the game. These two events have been the focus of a voluminous literature testing how restrictions in the baseball labor market (and their removal) aﬀected several variables, including player salaries, player mobility, and competitive balance, to name a few.

However, professional baseball did not always have a reserve clause. The reserve clause was formalized in 1887, before which baseball players had varying degrees of freedom in negotiating with other teams. This paper complements the existing literature by analyzing the impact of the newly implemented reserve clause on the salaries of a select number of players from the 1880s. The paper provides a unique contribution by investigating the other end of the reserve clause time line. Using rediscovered data from the 1880s, we estimate the impact of the reserve clause on average player salaries, remuneration to marginal product, and the premium paid to players when changing teams. To do so, we employ the two-step approach employed by Scully (1974). In the ﬁrst step, team revenue and production functions for the decade of the 1880s are estimated, from which it is possible to estimate each player’s marginal product and marginal revenue product. In the second step, a wage model is estimated in which the impact of the reserve clause is estimated, controlling for player productivity and other player attributes.

The evidence suggests that the binding reserve clause reduced the average sample player’s

1 salary by approximately 8-10% in the years immediately after it was implemented. Further, higher quality players were not able to negotiate their salaries higher in order to oﬀset the deleterious impact of the reserve clause on salaries. Finally, the reserve clause reduced, but did not eliminate, the premium paid to players for changing teams, at least in the ﬁrst three years of the policy. Thus, as quickly as the removal of the reserve clause allowed salaries to increase, it seems that instituting the reserve clause ninety years earlier had an immediate and opposite impact on player salaries.

2 The Reserve Clause: History and Literature Review

The professional era of baseball began in the early 1870s, culminating with the formation of the National League in 1876. As baseball transformed from an amateur game into a business, labor issues soon arose. Unlike present day baseball players, ﬁrst generation professional baseball players were not compensated as full-time, year-round professional athletes. In fact, management believed players should be employed elsewhere during the oﬀ-season months (Seymour 1960, p. 106). Not surprisingly, as teams competed for players, team expenses began to escalate.

Without the ability to coordinate hiring practices across different teams, owners thought that only the most wealthy teams or teams in the largest cities would monopolize the best player talent, threatening the financial viability of the entire league. Thus from the owners’ perspective, there was an impetus for a system that would prevent player salaries from increasing. As a result, what would eventually become the reserve clause was initiated in 1879. Intended to decrease expenses by placing limits on player salaries, the policy initially “reserved” only a few players on each team. While a reserved player was tied to one team unless the team owner decided otherwise, anecdotal evidence suggests that the initial reserve system was not as effective as team owners intended. Nevertheless, Burk (1994) described

2 the reserve system as “the most signiﬁcant step [up to that time] in a progression of moves to limit player independence and control” (p. 63).

During the 1880s two additional leagues were formed: the American Association (from 1882-1891) and the Union Association (for one year in 1884). As the new leagues increased competition for players, in 1883 the American Association and the National League jointly “agreed” to adhere to the reserve clause. Thus, the original reserve system evolved into a gentleman’s agreement in which players were included on each team’s reserve list by reference only (Spalding 1960), i.e., there were no contract stipulations concerning the reserve clause. This reserve system was slightly more effective but was difficult to enforce as there was little recourse if one team “poached” a player from another team. However, starting in 1887 the reserve clause was formally included in player contracts (Spalding, p. 109), making the enforcement of the system much easier. Once it was formalized in 1887, the reserve clause persisted until 1974, when baseball introduced final offer arbitration for players with at least three years of major league experience. This did shift some market power to players, although players were still tied to their teams indefinitely. In 1975, Andy Messersmith and Dave McNally sued Major League Baseball to become free agents.1 After several months of arbitration and court appearances, the two players were granted free agent status for the 1976 season, although only Messer- smith took advantage. Thereafter, free agency was introduced for players with more than six years of Major League Baseball experience, which expanded the already existing arbitration system. As predicted by economic theory, the shift of market power to the players caused a dramatic increase in the salaries of veteran players, and the clear regime changes in 1974 and 1976 have been the focus of numerous studies. 1This was not the first lawsuit concerning free agency. In 1970, Curt Flood, center fielder for the St. Louis Cardinals, sued Major League Baseball after he was involuntarily traded in 1969 to the Philadelphia Phillies. Curt Flood argued that Major League Baseball violated anti-trust statutes and sued for economic damages. Although he ultimately lost his case, it was heard by the U.S. Supreme Court and arguably galvanized players for future action against the reserve clause.

3 In the pre-free agency era, the seminal paper concerning the reserve clause was Rotten- berg’s (1956) theoretical analysis of baseball’s labor market. He examined the foundation and effects of the reserve clause and questioned the claim that the reserve clause was needed to prevent higher-revenue teams from dominating the market for high-quality baseball players. Rottenberg argued that teams eventually experience diminishing returns from hiring high-quality players. That is, ticket sales increase at a decreasing rate per “star” player added to the roster. In the pursuit of maximum profits, it is not in a team’s best interest to dominate other teams, since “no team can be successful unless its competitors also survive and prosper sufficiently so that differences in the quality of play among teams are not ‘too great’” (p. 254). Therefore, he concluded that without the reserve clause in place, players would go to where they are valued the most but not necessarily to the richest or largest market teams.

The literature focusing specifically on the early period of the reserve clause is very limited. Fort (2005) quite ably reviews and re-positions Rottenberg’s insights concerning the broad literature concerning the reserve clause. He undertakes a brief empirical investigation of how the reserve clause impacted competitive balance in the 1880s and finds adverse effects. Eckard (2001) also discusses the early period of the reserve system and provides empirical evidence suggesting that competitive balance was adversely affected by the reserve clause, inferring that the reserve system was a rent-protection scheme on the part of team owners.

A number of studies have focused on the impact of free-agency and arbitration on player salaries; in essence testing the extent to which removal of the reserve clause reduced monopsony power. Scully (1974) and Medoff (1976) compared estimated marginal revenue products to the salaries of players during the pre-free agency period. Both found that team owners had significant monopsony power. Sommers and Quinton (1982) found that the first wave of free agents in baseball were paid much closer to their estimated marginal revenue product, suggesting that the reserve clause was a binding limitation on player salaries; removing the

4 monopsony power of team owners led to an immediate increase in player salaries. Chelius and Dworkin (1980) were the first to estimate the impact of final offer arbitration (FOA) on salaries and found that FOA eligibility substantially increased player salaries, suggesting that the reserve clause conferred substantial monopsony power to team owners. Marburger (1994) found evidence that monopsony power was not completely eradicated with arbitration but that it was eroded over the years between arbitration eligibility and free-agency eligibility. To the extent that this literature provides a guide for this paper, it is anticipated that the binding reserve clause would have the opposite impact on player salaries than when it was removed.

3 The Reserve Clause in its Infancy: Testable Hy-

potheses

Consider each player’s salary as the outcome of a negotiation between the player, or his representative, and the team, or its representative. The contract zone, or negotiating space, can be deﬁned by two extremes (see Pigou, 1920, and Persky and Tsang, 1974). At the lower end is the player’s reservation wage, or the minimum salary for which he is willing to play, and at the upper end is the player’s marginal revenue product, or the maximum the team is willing to pay. The negotiation process yields an actual salary that can be considered a

r weighted average of the two extremes of the contract zone, i.e., wi = (1 − αi)wi + αiMRPi,

r where αi ∈ [0, 1] is an index of negotiating strength on the part of the player, Wi is the

2 player’s reservation wage and MRPi is the players marginal revenue product. The reserve clause was clearly aimed at reducing the negotiating strength of the players, that is to reduce αi for all players, regardless of skill. However, it is possible that the very best players in professional baseball might have overcome the loss of negotiating strength

2This formulation is similar to Marburger (1994).

5 brought about by the reserve clause by threatening to withhold their services from their team. Finally, if the Rottenberg conjecture is correct then the reserve clause allowed team owners to distribute player rents between themselves when a player moved to a new team, either through trade or sale, which would then reduce the premium received by the player for changing teams. Salary data for all players during the 1880s are not available, precluding a direct estimate of the negotiating strength of players and team owners. However, utilizing a unique and heretofore unused data set, we can test the impact of the introduction of the reserve clause on the salaries of a select group of high-quality players from the 1880s. The empirical exercise allows us to test whether the reserve clause materially shifted monopsony power to team owners immediately after its inception as reﬂected in a reduction in player salaries, ceteris paribus.

Three hypotheses about the inﬂuence of the reserve clause on player salaries are tested. First, did the binding reserve clause suﬃciently increase monopsony power such that the salary of the average player in the sample declined almost immediately? This hypothesis is tested against the following null hypothesis:

Hypothesis 1 The institution of the reserve clause did not cause a change in the average player’s salary, ceteris paribus.

Second, we test whether higher quality players were impacted by the reserve clause differently than lower quality players. We test this by estimating whether the reserve clause materially altered the return to marginal product. This hypothesis is tested against the following null hypothesis:

Hypothesis 2 The institution of the reserve clause did not cause a change in the remuneration to player marginal product, ceteris paribus.

Third, we test the Rottenberg (1956) invariance principle which posits that the reserve

6 clause allowed team owners to distribute the rents generated by a player among themselves, thereby reducing the premium paid to a player when he changed teams. The third hypothesis is tested against the following null hypothesis:

Hypothesis 3 The institution of the reserve clause did not cause a change in the premium paid to players when changing teams, ceteris paribus.

To test these hypotheses, we estimate two types of models: one with real player salary as the dependent variable and the other with the level of monopsony exploitation as the dependent variable, following Scully (1974).3 In both models we control for player characteristics, characteristics of the market for baseball labor, and characteristics of the overall economy so to isolate, to the extent possible, the inﬂuence of the reserve clause on the dependent variables.

4 Data, Model Speciﬁcations, and Empirical Results

The empirical analysis of player salaries necessarily requires a measure of each player’s marginal product. Only after controlling for the player’s quality is any accurate inference about the impact of the reserve clause on player salaries possible. In order to determine each player’s marginal revenue product, we follow the two-step approach pioneered by Scully (1974). The first step entails estimating team revenue as a function of team winning percentage and city and league fixed effects. The second step entails estimating a team production function where output is team winning percentage and the primary inputs are team offense and defense performance. After estimating the team production function, the contribution

3There are surprisingly few empirical studies that estimate monopsony exploitation although Pigou (1920) and Robinson (1934) spend considerable effort discussing the topic in a theoretical context. In addition to Scully’s study, Persky and Tsang (1974) analyzed the level of Pigouvian exploitation in the U.S. economy, relating the ratio of marginal product to real wages as a function of unionization, unemployment, inflation, the capital stock, and government imposed controls in the labor market. They found that exploitation increased with unemployment, inflation, the capital stock, and governmental intervention. The only variable negatively correlated with exploitation was unionization.

7 of a player to team winning percentage can be calculated. Combining this with the revenue function generates an estimated marginal revenue product for the player. The second stage of the analysis relates real salaries to player productivity, player characteristics, and general market characteristics.

The salary data employed in this analysis were obtained from an article published in 1914 in the now-defunct Baseball Magazine. Penned by Mr. William H. Dunbar, this short article titled “Baseball Salaries Thirty Years Ago,” lists the salaries of twenty-nine high-quality players from 1881 through 1889. The article discusses the salary issues during the 1880s, and points out that concerns over escalating baseball salaries in the 1910s were similar to those in the 1880s. Mr. Dunbar does not mention the reserve clause nor its impact on player salaries, but rather questions whether salaries are “too high” for the best players in the league.4 We combine Dunbar’s data, assuming that any errors are purely random, with the wealth of historical statistics gathered by baseball historians over the past several decades. The data provide a unique opportunity to test the inﬂuence of the reserve clause during its inception rather than the more common approach of testing the inﬂuence of removing the reserve clause after 1976.

A. Estimating Player Marginal (Revenue) Product

We ﬁrst estimate a team attendance (revenue) function:

DEPit = γ0 + γ1WIN80it + γ2WIN81it + γ3WIN82it + γ4WIN83it + γ5WIN84it

+ γ6WIN85it + γ7WIN86it + γ8WIN87it + γ9WIN88it + γ10WIN89it +

+ γ11CONT + φT EAM + θLEAGUE + vit, (1)

where DEPit is, alternatively, annual home game attendance or annual real total revenues

4Here, we need more information on Dunbar and his credibility.

8 for team i in year t, and vit is a zero mean heteroscedastic error structure that is tested for first order autocorrelation. We allow the marginal impact of team quality to change over the course of the 1880s by interacting winning percentage with year dummy variables. We also include a vector of team fixed effects (T EAM) and a vector of league fixed effects (LEAGUE) and a dummy variable that takes a value of one if the team finishes the season within five games of first place (CONT ).5 Real total revenue is calculated as team home attendance times $0.50 which is then adjusted to reflect 2004 dollars.6 The results from estimating equation (1) provide evidence of the additional attendance or revenue from an additional point in winning percentage, the latter is used to determine the marginal value of an additional point of winning percentage. Winning percentage is, in turn, the outcome of team defensive and offensive performance, managerial decisions, and idiosyncratic influences such as injuries, team cohesion, and weather. The value of a player is therefore connected to team attendance or revenue through the player’s contribution to team winning; players contribute to team winning percentage through their individual offensive and defensive contributions. Field position players provide defensive output in the form of fielding, assists, and put-outs, and offensive output in the form of hits, stolen bases, and sacrifices. Pitchers contribute through stikeouts, innings pitched, reduced numbers of earned runs allowed, and, to a lesser extent, the offensive and defensive contributions of regular field players. While a large literature investigates various ways of modeling baseball team production functions (e.g., MacDonald and Reynolds (1994) and Bradbury (2007)), we use two team-level measures of offensive and pitching performance: slugging average and team strikeout-to-walk ratio, respectively.7

5This variable was included in the production function in Scully (1974). 6Total home game attendance were collected from The Baseball Encyclopedia. In general, team prices are not available from this era however the National League agreed to ﬁx gate prices at $0.50 in 1879. The price of attendance to National League baseball games played in the Polo Grounds in New York was ﬁfty cents for the 1903, 1904, 1905 and 1906 baseball seasons (New York Times, various editions). We assume that the other teams in the other leagues charged the same price as the National League. 7Alternative production functions have been investigated in the literature. MacDonald and Reynolds (1994) use runs scored and earned run average as the primary inputs to winning whereas Bradbury (2007)

9 The production function is speciﬁed as:

WINPCTit = β0 + β1TSAit + β2TSWit + β5NLit + β6UAit + ²it, (2)

where the β’s are parameters to be estimated and ²it is a composite zero-mean heteroscedastic error term.8 The dependent variable is team win percentage, which normalizes team performance by the number of games a team played; games played varied during the sample period. The independent variables include the team slugging average (TSA), team strikeout- to-walk ratio (TSW), a dummy variable that takes a value of one if the team played in the National League (NL), and a dummy variable that takes a value of one if the team played in the Union Association (UA).9

The top panel of Table 1 presents the descriptive statistics for the team data employed in estimating equations (1) and (2). The average season attendance for teams during this period was approximately 106,000 and average real gate revenues were approximately $960,000.10 The average winning percentage is less than 500 because during the 1880s teams often did not play the same number of games. The average team slugging average was .336 and the average strikeout-to-walk ratio was 2.15. Approximately 20% of all teams finished within 5 uses the difference between runs scored and runs allowed, arguing that earned run average is not a good measure of pitching quality as the measure depends on the quality of a team’s defense, which is beyond control of the pitcher. We estimated our models using these alternative inputs and found qualitatively similar results. 8Scully’s production function included two additional variables: a dummy variable that took a value of one if the team finished the season within five games of first place (CONT ) and another that took a value of one if the team finished more than twenty-five games out of first place (OUT ). These two variables have been criticized by some authors, e.g., Baol and Ransom (1997). In our specification, we suppress these two variables. 9Slugging percentage is defined as the total bases obtained by the team divided by the total number of at-bats. Team and player data were obtained from www.baseballreference.com, last accessed August 2008. 10Teams in the 1880s did generate very little additional revenue through concession sales. Moreover, at the time there were no media, merchandise or stadium revenue, nor was there league revenue sharing, thereby avoiding one of the criticisms of using team total revenue offered by Krautman (1999). We do not anticipate the measurement error in our estimate of real total revenue to prove debilitating to the estimation results reported herein.

10 games of first place. Table 2 reports the estimation results of four versions of equation (1): the first two use attendance as the dependent variable, the second two use real gate revenue. For each dyad of models we report two specifications: robust OLS and random effects with panel specific heteroscedasticity. Our primary focus is on revenues but as revenues were directly related to attendance, we report the attendance equations for completeness. The results indicate that over the decade of the 1880s the marginal impact of an additional point of winning percentage on attendance and hence real revenues steadily increased, except for the economic downturn in 1888. Teams in the National League generally fared no differently than the American Association teams, although the American Association disbanded in 1889. However, teams in the Union Association, which existed only for the year of 1884, experienced dramatically less attendance than American Association teams and hence also experienced dramatically less revenue. Finally, teams in contention enjoyed considerably higher attendance and real revenues, as expected. Overall, the results in Table 2 point to an increasing popularity of professional baseball which led to dramatic increases in the real revenues generated by successful teams.

Table 3 reports the results from estimating equation (2) using two different estimators: robust OLS and team random effects, although the random effects model is supported over robust OLS via a Lagrange Multiplier test. From Model (2) the marginal win percentage (on a scale of 0 to 1000) associated with a one unit change in team slugging average (on a scale of 0 to 1000) is 2.169, while a one unit change in team strikeout-to-walk ratio corresponds to an approximate 23 percentage point increase in win percentage. Teams that played in the National League and the Union Association fared relatively worse than their American

Association counterparts, ceteris paribus. The team production function is used to calculate the marginal product of the players

11 in the sample.11 Using the results from Model (2) of Table 3, each player’s marginal win percentage (MWP) is calculated as

MWPit = (SAit × P ERABit × 2.169 × 1000) + (SWit × PERSOit × 38.467),

where SWit is set to zero for non-pitchers. This approach is not immune from criticism. It is “proportional” in that a player is only given credit for a portion of his total offensive and defensive production. Zimbalist (1992) recommends an “incremental” approach which measures the change in a team’s performance with and without a player. The proportional approach relies upon estimated revenue functions to indirectly determine marginal revenue product, whereas Krautman (1999) recommends directly estimating the value of various offensive and defensive categories using a well-operating free-agent market. However, the direct approach is not appropriate for the 1880s because of data limitations. Furthermore, while Krautman did not estimate MRP for pitchers, the proportional approach provides an estimated marginal product for pitchers.12 There is also a debate as to whether the strikeout-to-walk ratio is an appropriate measure of pitcher contribution; some authors have instead used earned run average (ERA). However, as Bradbury (2007) shows, the ERA is vulnerable to influences beyond the control of the pitcher and is not highly correlated from year to year. This suggests the ERA is not an ideal measure of a pitcher’s marginal contribution to team success. The methodology used here assures non-negative marginal products and arguably better captures the contribution of a pitcher to his team’s success.13

11See the appendix for an extended discussion on exactly how to calculate a player’s marginal product. 12Krautman did not investigate the MRP of pitchers arguing that pitchers in the modern era are often specialists, i.e., starters, closers, or set-up men, and therefore the appropriate measure of a pitcher’s productivity is less clear than for position players. Furthermore, the Krautman approach would sacriﬁce 40% of our sample, which seems excessive given its already limited size. 13Pitchers in the 1880s were less specialized than in the modern era. Furthermore, including ERA and other pitching statistics directly into the team production function yields negative marginal products for numerous players.

12 B. Estimating the Impact of the Reserve Clause on Player Salaries

The marginal product of a player is not known until after the season is completed whereas the player’s salary was (and is) typically determined at the beginning of the season. Therefore, we assume that a player’s previous season’s marginal win percentage (marginal product) is a rational proxy for the marginal win percentage in the current year. To test whether the binding reserve clause inﬂuenced real player salaries as hypothesized in the previous section, various wage models are estimated. Their general functional form is:

2 DEPjt = δ0j + δ1MWPjt−1 + δ2Experiencejt + δ3Experiencejt + δ4NewT eamjt

+ δ5NewLeaguejt + δ6MacroIndext + δ7RCt

+ δ8RCt × MWPjt−1 + δ9RCt × NewT eamjt + θTjt + ujt, (3)

where j indexes players, t indexes time, ujt is a zero-mean composite error term, and the δ’s and the vector θ are parameters to be estimated. The dependent variable is real salary converted to 2004 dollars using the Bureau of Labor Statistics Consumer Price Index, or the ratio of estimated real marginal revenue product to real wage, where real marginal revenue product is calculated as the product of the player’s marginal win percentage and the appropriate yearly parameter from Model (4) in Table (2).14

The explanatory variables include the player’s previous year’s marginal win percentage (MWP ), anticipating that more productive players are compensated more. We control for the player’s major league experience up to the current year (Experience), and its quadratic (Experience2), anticipating that a player’s experience might enhance his negotiating power

14There are potentially negative effects of using a ratio as the regressand (see Kronmal, 1993, for example), including possible specification bias. On the other hand, any measurement error in the estimated real marginal product is shifted to the left hand side of the estimating equation, where it is expected to only influence the efficiency of the estimates.

13 relative to a team owner either as his true value is revealed over time or he gains negotiating experience. We also control for whether the player changed teams (NewT eam) and whether the player changed leagues (NewLeague). In the pre-reserve clause era, a player would be expected to receive a premium for changing teams. However, it is less obvious that there would be a premium when changing leagues. Given the short life of many teams and leagues during the early history of professional baseball, many players who changed leagues did so while being “unemployed” rather than “just looking” ball players, which might have reduced their subsequent wages. To control for the general conditions of the labor market for baseball, we introduce a dummy variable that takes a value of one after the reserve clause became binding (RC). We control for the overall health of the macroeconomy, which might proxy for baseball players’ opportunity costs, using the NBER’s U.S. Index of Manufacturing Production (MacroIndex)15 Finally, the vector T contains team-specific dummy variables that take a value of one if a player is on a given team and zero otherwise. To test Hypothesis 1, we include the RC dummy variable as a separate regressor. If the reserve clause reduced the negotiating stance of the players in the sample, on average, we anticipate a negative parameter estimate on this variable. To test Hypothesis 2, the dummy variable RC is interacted with the player’s estimated MWP. If higher quality players were able to offset any negative influence of the reserve clause on negotiating power, we would expect the parameter on this interaction term to be positive. Finally, to test Hypothesis 3, the Rottenberg (1956) conjecture, we interact the RC dummy variable with NewT eam. If the binding reserve clause caused player rents to be shared more between owners rather than between owner and player, we anticipate a negative parameter estimate on this variable.

The bottom panel of Table 1 presents the descriptive statistics of the data used to estimate equation (6). During the sample period the average nominal salary was $2,461 ($45,872 in 2004 dollars). Because the players in the sample were amongst the best players of the day,

15We acknowledge Brad Humphreys for this valuable suggestion. During the sample period there were two peaks (March 1882 and March 1887) and two troughs (May 1885 and April 1888) in the business cycle.

14 it is likely that the sample average is greater than the overall Major League average salary. The average MWP was 46 points, the average player’s estimated MRP was $90,444, and the average player’s ratio of MRP to wage was approximately two. The average player in the sample had 5.8 years of experience, approximately 18 percent of the observations correspond to a player that switched teams from one season to the next, approximately 3 percent of the observations corresponded to players that switched leagues from one season to the next, and approximately 43 percent of the sample observations correspond to the period during which the binding reserve clause pertained. Finally, the NBER manufacturing index (1909 − 1913 = 100) averaged 33.274, but did show a considerable range during the sample period.

The δ0j in equation (3) reflect player-specific unobserved or unmeasured heterogeneities that might influence the outcome of a player-team salary negotiation. Because the sample reflects only a subset of the players in the major leagues at the time, the player-specific effects are treated as random effects. Table 4 reports estimation results in which only player-specific random effects are included, i.e. restricting θ = 0. Table 5 and Table 6 report estimation results including player random effects and the team dummy variables, the latter reflecting team-specific premiums paid to players during the sample period.

C. The Reserve Clause and Player Salaries: Empirical Results and Discussion

Model (1) in Table 4 is a base model which includes no controls concerning the reserve clause; the dependent variable is real salary in 2004 dollars. Given the limited sample size and its historical nature the results are encouraging; the estimated parameters have the expected sign and are generally statistically signiﬁcant. The average player was paid more as he was more productive, suggesting that players were able to extract some of the value they created for team owners. Players were paid more with more experience, although at a decreasing rate. Players were paid a premium when changing teams but sacriﬁced salary when changing

15 leagues. Finally, real salaries were positively related to the the NBER manufacturing index. The ﬁrst three models in Table 4 use real salary as the dependent variable, the last three use exploitation as the dependent variable. Model (1) and Model (4) are baseline models in the sense that they do not control for the reserve clause system at all. Model (2) and Model (5) add the reserve clause dummy variable. Model (3) adds the interaction term between RC and MWPt−1 and between RC and NewT eam, whereas Model (6) only adds the interaction between RC and NewT eam as MWP is not included on the right side of Models (4)-(6).16 The binding reserve clause corresponded with an economically and statistically signiﬁcant reduction in the average sample player’s salary, anywhere between $3,000 to $5,000, ceteris paribus. Given the sample mean salary of approximately $45,000, the reserve clause reduced the average sample salary by approximately 8-11%. The models in which exploitation is the dependent variable provide a consistent story: after the binding reserve clause was instituted, the ratio of real marginal revenue product and real wages increased, suggesting a reduced negotiating stance for the players in the sample.

The results from Model (3) in Table 4 suggest that higher quality players were unable to alter their wages after the binding reserve clause relative to similar quality players before the reserve clause, however the remuneration to marginal product didn’t fall either. The parameter on the interaction between the NewT eam and RC lends support to the Rottenberg conjecture. In Model (3), switching to a new team after the reserve clause was instituted had an approximately $5,500 lower premium than before the reserve clause. While the results in Table 4 are encouraging and in many ways seem conclusive given the limited scope of the data sample employed, there are at least two potential areas of concern. First is a concern of sample selection. Were players chosen because of their fame and name recognition? In one attempt to control for selection bias, we used whether the player was

16We experimented with including the MWP on the right-hand side of the speciﬁcations using exploitation as the dependent variable. However, the results were unsatisfactory as the variable MWP is essentially included in the numerator of the dependent variable.

16 of foreign birth, whether the player was from the Southern United States, and whether the player was in the top ten in terms of home runs, runs scored, or earned run average, to identify whether the player’s salary was reported. In this approach, the inverse Mills ratio was consistently insignificant. In another approach, we controlled for possible selection bias based on the teams for which salaries were reported. We used the age of the franchise and the state in which the franchise played to identify selection. The inverse Mills ratio was again consistently insignificant, suggesting that selection bias (at least based on the identification employed) is not a significant problem.

Another concern is potentially omitted variables, from both the supply and demand sides. Although the specifications in Table 4 include player-specific effects, which control for unobserved player-specific heterogeneity, there might be concerns that team-specific or city-specific effects have been excluded. Table 5 and Table 6 report estimation results that address this problem. Specifically, we ask a little more from the 200 observations and include 12 team fixed effects (Buffalo, from the National League, is the reference team).

Table 5 reports the estimation results including team fixed effects. By including the team specific effects, inference is weakened as another 6% of the sample size is sacrificed. The impact of the reserve clause on the average sample salary (and average level of exploitation) is still negative (positive), consistent with the results in Table 4. Further, the impact of the reserve clause on the amount players were paid for the marginal product remains insignificant. The statistical significance of the interaction between NewT eam and RC is lost when including the team fixed effects. While the parameters carry the same sign, although not the same magnitude, the standard errors are considerably larger than when the team fixed effects are restricted to zero. This suggests that some of the reduced premium for changing teams reported in Table 5 might have been caused by the teams involved with the trades. The remaining parameters are all of the same sign, magnitude, and significance as before.

Table 6 reports the team fixed effects, which reflect premiums the teams paid players

17 relative to the reference team, ceteris paribus. Any differences in the team fixed effects are reduced form and therefore reflect both demand and supply-side effects, including differences in the costs of living, differences in reservation wages for playing in a large or small city, or a weak negotiating stance on the part of the team owners in certain cities.17

Looking at the estimated team eﬀects, an interesting pattern emerges. First, almost all of the teams in the sample paid a premium over the reference team of Buﬀalo; the exception is

Providence and the greatest premiums were paid by (in descending order) Washington, New York of the American Association, Boston and New York of the National League.18 This suggests city size might be an important factor to the premium a player received during the 1880s. Table 6 reports the population rank of the various host cities for 1880 and 1890.19

Figure 1 shows a plot and ﬁtted simple regression line of the estimated team premiums from Model (3) in Table 6 against the population rank of the host city in 1890. Indeed, there is a slight positive correlation between the population rank of the city (low number indicating a greater population) and the premium paid to the average player (ρ = −0.36 in both 1880 and 1890).

17The “microscope effect” occurs when a player demands a premium for playing in a city in which he will receive considerably more attention and scrutiny. Some players demand a compensating differential for the additional pressure such scrutiny entails. This is arguably one component to the inflated salaries for modern-era players in New York and Boston, for instance. Whether the microscope effect would have pertained to professional baseball in the 1880s is not clear. Newspaper accounts of the day do not focus much on the off-field behavior of players and there is virtually no mention of baseball players during the off-season. 18Anecdotal evidence suggests that teams in New York, Boston, and Baltimore (the closest team to Washington between 1972 and 2005) all pay substantial premiums to players. Examples include Sammy Sosa playing for the Baltimore Orioles, Alex Rodriguez playing for the New York Yankees, and Manny Ramirez playing for the Boston Red Sox. All of these players were alleged to have been paid considerably more for their quality of play than they would have been paid in other cities. 19Population counts were obtained from the U.S. Census Bureau.

18 5 Conclusions

Using a unique data set describing the salaries of 29 high-quality players from 1881 through 1889, three hypotheses concerning the impact of the introduction of the binding reserve clause in Major League Baseball in 1887 are tested. Following the two-step approach of Scully (1974) it is shown that the binding reserve clause corresponded with a decrease in the average sample salary by approximately 10%. It is also documented that players with higher quality were not able to overcome the deleterious impact of the binding reserve clause in their negotiations with team owners. It is also shown that after the binding reserve clause, the premium players received when changing teams fell by almost 50% on average, lending support to the Rottenberg (1956) conjecture that the reserve clause allowed team owners to redistribute player rents among themselves. The results are consistent with the reserve clause shifting considerable monopsony power to baseball team owners immediately after its inception, the exact opposite of what happened in 1976 when the removal of the reserve clause almost immediately shifted detectable market power back to the players.

19 References

Boal, William M. and Michael R. Ransom (1997). “Monopsony in the Labor Market,” Journal of Economic Literature, 35(1), 86-112.

Bradbury, John Charles (2007). “Does The Baseball Labor Market Properly Value Pitch- ers?” Journal of Sports Economics, 8(6), 616-632.

Burk, Robert F. (1994). Never Just a Game: Players, Owners, and American Baseball to 1920, Chapel Hill: The University of North Carolina Press.

Chelius, James R. and James B. Dworkin (1980). “An Economic Analysis of Final-Offer Arbitration as a Conflict Resolution Device,” Journal of Conflict Resolution, 24, 293- 310.

Dunbar, William H. (1914). “Baseball Salaries Thirty Years Ago,” Baseball Magazine, July, 291-292.

Eckard, E. Woodrow (2001). “The Origin of the Reserve Clause: Owner Collusion Versus ‘Public Interest,’ ” Journal of Sports Economics, 2, 113-130.

Fort, Rodney (2005). “The Golden Anniversary of ‘The Baseball Players Labor Market’,” Journal of Sports Economics, 6, 347-358.

Krautman, Anthony C. (1999). “What’s Wrong with Scully-Estimates of a Player’s Marginal Revenue Product?” Economic Inquiry, 37, 369-381.

Kronmal, Richard A. (1993). “Spurious Correlation and the Fallacy of the Ratio Standard Revisited,” Journal of the Royal Statistical Society. Series A (Statistics in Society), 156, 379-392.

MacDonald, Don N. and Morgan O. Reynolds (1994). “Are Baseball Players Paid Their Marginal Products?” Managerial and Decision Economics, 15(5), 443-457.

Marburger, Daniel (1994). “Bargaining Power and the Structures of Salaries in Major League Baseball,” Managerial and Decision Economics, 15, 433-441.

Medoﬀ, Marshall H. (1976). “On Monopsonistic Exploitation in Professional Baseball,” Quarterly Review of Economics and Business, 16, 113-121.

Persky, Joseph and Herbert Tsang (1974). “Pigouvian Exploitation of Labor,” The Review of Economics and Statistics, 56(1), 52-57.

Pigou, Arthur C. (1920). The Economics of Welfare, London: Macmillan and Co.

Robinson, Joan (1933). The Economics of Imperfect Competition, 2nd edition (1969), Palgrave Macmillan.

20 Rottenburg, Simon (1956). “The Baseball Players’ Labor Market,” The Journal of Political Economy, 64, 242-58.

Scully, Gerald W (1974). “Pay and Performance in Major League Baseball,” The American Economic Review, 64, 915-30.

Seymour, Harold (1960). Baseball: The Early Years, New York: Oxford University Press.

Sommers, Paul M. and Noel Quinton (1982). “Pay and Performance in Major League Baseball: The Case of the First Family of Free Agents,” Journal of Human Resources, 17, 426-436.

Spalding, Albert G. (1991) Base Ball: America’s National Game 1839-1891, Edited by Samm Coombs and Bob West. San Francisco: Halo Books.

21 Appendix

A player’s slugging average does not have a one-to-one relationship with the team’s slugging percentage; the marginal product from the team production function overstates the marginal product of an individual player’s oﬀensive or pitching contribution. To see this, note that team slugging percentage can be written as P P P P i Hik + i Dik + 2 i Tik + 3 i HRik TSAk = P , (4) i ABik where i = 1 ...Nk indexes the number of players on team k, H is the number of hits (of any kind), D is the number of doubles, T is the number of triples, and HR is the number of homeruns hit by the players on the team, and AB is the number of at-bats by the players on the team. An individual player’s slugging average is:

Hi + Di + 2Ti + 3HRi SAi = , (5) ABi which can be rewritten as

ABiSAi = Hi + Di + 2Ti + 3HRi. (6)

Summing both sides of equation (6) over the N players on team k one obtains: X X X X X ABikSAik = Hik + Dik + 2 Tik + 3 HRik. (7) i i i i i P The right hand side of equation (7) equals TSAk × i ABik so that the team’s slugging average can be written as X X ABikSAik = TSAk ABik. i i This, in turn, suggests that the marginal impact of a player’s slugging average on team slugging percentage can be written as:

∂T SAk ABi = P dSAi, ∂SAi i ABik where the first term is the percentage of a team’s at-bats for player i and dSAi is the change in a player’s individual slugging percentage.20 For non-pitchers, slugging average captures their contribution to team win percentage. However, during the 1880s all pitchers hit, and therefore pitchers contributed to team win percentage through their offensive and pitching efforts.

20This result is alluded to, but not derived, by Chelius and Dworkin (1980) and Krautmann (1999).

22 It is possible to derive the marginal impact of a pitcher’s individual strikeout-to-walk ratio on the team’s strikeout-to-walk ratio as:

∂T SWk Ki = P dSWi. ∂SWi i Kik An individual pitcher’s contribution to the team strikeout-to-walk ratio is the product of that pitcher’s strikeout-to-walk ratio and the percentage of team strikeouts for which the pitcher accounted. Combining the two derivatives it is possible to calculate each player’s marginal win percentage as:

MWPit = (SAit × P ERABit × MPTSA) + (SWit × PERSOit × MPTSW ), where SAit denotes player i’s slugging average in year t, P ERABit denotes player i’s percentage of team at-bats in year t, MPTSA denotes the marginal product of team slugging percentage, SWit denotes player i’s strikeout-to-walk ratio (pitched) in year t, PERSOit denotes player i’s share of team strikeouts pitched in year t, and MPTSW is the marginal product of team strikeout-to-walk ratio.

23 Table 1: Descriptive Statistics of the Data

Team Data (1880-1889)

Variable Description Mean Std.Dev. Min Max

WinPer Team win percentage 488.40 139.52 171.71 824.56 Attendance Team home attendance 105,691.30 73,148.44 11,000 353,690 TR Real total Revenue 963,854.40 695,471.50 91,049.99 3,393,656 TSA Team slugging average 336.47 36.71 253.03 445.71 TSW Team strikeout-to-walk ratio 2.15 1.34 0.56 10.69 CONT Less than ﬁve games from ﬁrst 0.19 0.39 0 1 NL Team played in National League 0.51 0.50 0 1 UA Team played in Union Association 0.06 0.22 0 1 AA Team played in American Association 0.43 0.49 0 1 Obs/Teams 154/40

Player Data Variable Description Mean Std.Dev. Min Max

SALARY Nominal salary 2,461.38 989.13 875 7,000 RSALARY Real salary (2004 dollars) 45,871.65 19,116.55 15,373.75 131,040 lnSALARY Log of real salary 10.64 0.47 9.64 11.78 MRP Estimated MRP (2004 dollars) 90,444.55 46,867.80 3,561.16 257,690.50 EXP LOIT Exploitation= MRPi/wi 2.04 0.93 0.17 6.67 RC Binding reserve clause (1887-1889) 0.43 0.49 0 1 MWP Marginal Win Percentage 45.67 20.83 1.85 154.70 Experience Player experience in years 5.85 3.72 0 18 Experience2 Quadratic of experience 48 59.40 0 324 NewT eam Player changed teams 0.18 0.38 0 1 NewLeague Player changed leagues 0.03 0.17 0 1 MacroIndex Index of Manufacturing Production 33.31 3.35 26.8 38.60 Obs/Players 200/29 Notes: Average team win percentage doesn’t equal 500 because only teams with at least ﬁfty games played are included. Strikeout-to-walk ratio measured in hundredths. Certain dummy variable means do not sum to one because of rounding. NBER Manufacturing Index obtained at http://www.nber.org/databases/ macrohistory/rectdata/01/a01007a.dat and was originally provided in Persons (1931), 1909-1913=100.

24 Table 2: Team Attendance and Revenue Functions (1880-1889)

Attendance Real Total Revenue OLS RE OLS RE WIN80 50.080* 37.842* 438.897 332.178* (1.70) (1.91) (1.61) (1.85) WIN81 61.891* 30.810 541.811* 263.697 (1.97) (1.46) (1.87) (1.39) WIN82 91.581*** 52.840** 801.048** 451.327** (2.67) (2.57) (2.55) (2.42) WIN83 173.792*** 122.396*** 1,546.366*** 1,080.864*** (3.49) (5.55) (3.43) (5.39) WIN84 140.753*** 115.665*** 1,288.205*** 1,052.517*** (4.03) (8.64) (4.01) (8.52) WIN85 173.434*** 151.189*** 1,613.757*** 1,409.394*** (4.95) (7.48) (4.97) (7.58) WIN86 245.093*** 238.576*** 2,338.396*** 2,285.161*** (6.45) (12.0) (6.59) (12.5) WIN87 314.248*** 279.615*** 2,959.863*** 2,636.768*** (5.95) (11.5) (6.01) (11.7) WIN88 271.149*** 238.671*** 2,551.295*** 2,260.641*** (5.48) (9.45) (5.54) (9.57) WIN89 312.320*** 298.393*** 3,017.692*** 2,875.438*** (6.47) (24.3) (6.62) (25.1) NL -6,137.845 -6,181.081 -52,630.845 -54,999.000 (-0.65) (-1.27) (-0.60) (-1.22) UA -40,515.257*** -34,937.384*** -367,172.732*** -313,422.886*** (-2.88) (-6.43) (-2.85) (-6.24) CONT 18,625.657 31,060.686*** 167,922.853 281,357.508*** (1.17) (3.76) (1.13) (3.72) Constant 11,612.916 16,507.349*** 100,980.637 145,723.692*** (0.85) (2.85) (0.80) (2.73) OLS vs. RE 55.54*** 55.98*** R2 0.58 0.59 Obs/Teams 157/43 157/43 157/43 157/43 Notes: Data describe 157 major league baseball teams from 1880 through 1889. Attendance data obtained from the Baseball Encyclopedia and real total gate revenue calculated assuming ticket prices of $0.50 and converted to 2004 dollars. Model (2) and Model (4) controls for panel-specific heteroscedasticity. Robust z statistics in parentheses. * significant at 10%; ** significant at 5%;*** significant at 1%

25 Table 3: Team Production Functions (1880-1889)

(1) (2) OLS R.E. TSA 2,186.836*** 2,169.630*** (9.09) (11.1) TSW 36.627*** 38.467*** (3.91) (8.30) NL -26.957 -22.988* (-1.57) (-1.65) UA -101.803** -96.053*** (-2.57) (-3.71) Constant -306.089*** -314.142*** (-3.51) (-4.99) OLS vs. RE 12.74*** R2 0.47 . Obs/Teams 157/43 157/43 Notes: Dependent variable is team winning percentage. Data describe 157 professional baseball teams from 1880 through 1889 that played more than 50 games in a par- ticular year. Independent variables are defined in Table 1. Model (3) controls for panel-specific heteroscedasticity. Robust t statistics in parentheses. * significant at 10%; ** significant at 5%; *** significant at 1%

26 Table 4: The Reserve Clause and Player Salaries: Panel Estimation Results (No Team Fixed Eﬀects) (1) (2) (3) (4) (5) (6) RSALARY RSALARY RSALARY EXP LOIT EXP LOIT EXP LOIT MWP 100.903*** 86.159*** 74.977*** (5.56) (5.84) (4.59) Experience 2,487.285*** 3,039.037*** 3,081.237*** 0.073 0.097 0.099 (4.46) (4.12) (4.22) (0.91) (1.16) (1.18) Experience2 -61.329* -89.867* -88.760* -0.006 -0.008 -0.008 (-1.74) (-1.84) (-1.87) (-1.27) (-1.60) (-1.64) New Team 10,145.170*** 7,633.404*** 9,910.980*** -0.517*** -0.468*** -0.316 (5.74) (6.12) (6.73) (-2.93) (-2.81) (-1.49) New League -15,191.534*** -13,559.766*** -12,522.555*** 0.790 0.729 0.719 (-3.61) (-4.96) (-4.58) (1.32) (1.29) (1.27) Macro Index 2,988.417*** 2,777.528*** 2,763.900*** 0.154*** -0.006 0.002

27 (15.4) (9.62) (9.52) (5.38) (-0.14) (0.047) RC -3,368.889** -5,146.517** 1.312*** 1.363*** (-2.33) (-2.18) (5.08) (5.24) MWP × RC 36.254 (1.35) New Team × RC -5,388.328** -0.409 (-2.47) (-1.21) Constant -76,857.643*** -69,733.733*** -69,243.770*** -2.573*** 2.135* 1.867 (-11.7) (-7.74) (-7.58) (-2.98) (1.74) (1.49) ρ 0.61 0.62 0.63 0.51 0.48 0.29 Observations 200 200 200 200 200 200 Number of players 29 29 29 29 29 29

Notes: Dependent variables are player’s salary in 2004 dollars (RSALARY ) and Exploitation = MRPi/wi (EXP LOIT ). Inde- pendent variables are defined in Table 1. The sample is an unbalanced panel of 200 observations for 29 players from 1881-1889. Each specification includes player random effects, controls for panel-specific heteroscedasticity, and a common AR(1) error structure. Absolute value of robust t statistics in parentheses. * significant at 10%; ** significant at 5%. Table 5: The Reserve Clause and Player Salaries: Panel Estimation Results (Including Team Fixed Effects) (1) (2) (3) (4) (5) (6) RSALARY RSALARY RSALARY EXP LOIT EXP LOIT EXP LOIT MWP 85.456*** 89.340*** 77.608*** (5.77) (6.04) (4.61) New League -14,878.365*** -14,383.444*** -15,007.601*** 0.990* 0.810 0.818 (-5.34) (-5.19) (-5.15) (1.65) (1.44) (1.46) Experience 4,348.619*** 4,402.116*** 4,410.019*** -0.016 0.040 0.036 (7.10) (7.20) (7.27) (-0.18) (0.46) (0.41) Experience2 -157.373*** -158.561*** -160.221*** -0.001 -0.004 -0.004 (-4.16) (-4.16) (-4.23) (-0.13) (-0.78) (-0.74) New Team 6,781.645*** 6,669.627*** 7,067.505*** -0.403** -0.367* -0.405* (5.68) (5.58) (4.81) (-2.02) (-1.87) (-1.76) Macro Index 1,785.547*** 2,012.868*** 2,032.813*** 0.199*** 0.019 0.020

28 (7.31) (6.90) (7.08) (4.76) (0.36) (0.39) RC -2,470.690* -5,486.020** 1.334*** 1.314*** (-1.80) (-2.23) (5.14) (5.00) MWP × RC 39.351 (1.50) New Team × RC -623.621 0.147 (-0.26) (0.35) Constant -51,938.587*** -59,288.176*** -58,609.479*** -3.770*** 1.407 1.382 (-7.59) (-7.03) (-6.99) (-3.40) (0.98) (0.96) ρ 0.49 0.51 0.45 0.44 0.44 0.25 Observations 200 200 200 200 200 200 Number of players 29 29 29 29 29 29

Notes: Dependent variables are player’s salary in 2004 dollars, RSALARY and Exploitation = MRPi/wi, EXP LOIT . Independent variables are defined in Table 1. The sample is an unbalanced panel of 200 observations for 29 players from 1881-1889. Each specification includes player random effects and team fixed effects (reported in Table 4) and controls for panel-specific heteroscedasticity and a common AR(1) error structure. Absolute value of robust t statistics in parentheses. * significant at 10%; ** significant at 5%. Table 6: Team Fixed Effects from Table 4 Regressions

Pop Rank (1) (2) (3) (4) (5) (6) Team (LG) 1880/1890 RSALARY RSALARY RSALARY EXP LOIT EXP LOIT EXP LOIT Boston (NL) 5/6 19,188.865*** 19,484.306*** 19,121.561*** -0.695 -0.539 -0.566 (6.65) (6.72) (6.52) (-1.50) (-1.17) (-1.21) Chicago (NL) 4/2 7,741.499*** 7,861.031*** 7,366.564*** 0.141 0.272 0.283 (3.41) (3.45) (3.27) (0.47) (0.89) (0.93) Detroit (NL) 18/15 15,656.520*** 15,870.831*** 15,277.445*** 0.316 0.258 0.274 (6.85) (6.97) (6.56) (1.09) (0.85) (0.89) Indianapolis (NL) 24/27 8,802.125** 8,890.973** 7,917.349* 0.098 0.419 0.312 (2.02) (2.22) (1.91) (0.086) (0.43) (0.31) New York (AA) 1/1 23,417.329*** 23,397.436*** 23,225.259*** -0.578 -0.334 -0.330 (2.83) (2.86) (2.91) (-0.62) (-0.37) (-0.37) New York (NL) 1/1 19,422.578*** 19,608.144*** 19,106.119*** -0.402 -0.203 -0.199 (6.57) (6.67) (6.49) (-1.20) (-0.58) (-0.57) 29 Philadelphia (NL) 2/3 7,409.552** 7,928.304*** 7,455.956** 0.557 0.749* 0.755* (2.53) (2.71) (2.55) (1.28) (1.79) (1.80) Pittsburgh (AA) 12/13 14,619.018*** 13,678.663*** 12,870.165*** -0.416 0.084 0.137 (3.94) (3.65) (3.29) (-0.47) (0.098) (0.16) Pittsburgh (NL) 12/13 10,482.819*** 10,905.525*** 10,929.714*** -0.813 -0.688 -0.752 (3.02) (3.13) (3.08) (-1.57) (-1.32) (-1.38) Providence (NL) 20/25 9,670.035 9,214.758 9,736.567 0.552 0.865 0.850 (1.39) (1.32) (1.40) (0.73) (1.15) (1.14) Troy (NL) 29/46 8,747.060** 9,399.946** 9,084.903** -0.689 -0.846 -0.865* (2.30) (2.53) (2.41) (-1.36) (-1.63) (-1.67) Washington (NL) 14/14 23,666.820*** 24,953.242*** 25,826.115*** -2.153*** -2.175*** -2.172*** (5.85) (5.91) (5.92) (-3.37) (-3.03) (-3.04)

H0: Jointly Equal 118.40*** 119.75*** 111.25*** 40.60*** 39.16*** 38.55*** Notes: Column numbers correspond with models from Table 5. Reference team is Buffalo (NL), which ranked 13/11 in population size in 1880/1890. League abbreviations: NL - National League; AA - American Association. City population ranks obtained from the U.S. Census Bureau at http://www.census.gov/population/www/documentation/twps0027.html. Parameter values represent team-specific salary premiums above or below the reference team. Absolute value of robust t statistics in parentheses. * significant at 10%; ** significant at 5%. Figure 1: Estimated Team Salary Premiums vs. Host City Population Rank in 1890

WASN

25000 NYAA

NYN BOSN 20000

DETN

15000 PITAA PITN PRON TRON 10000 INDN CHINPHIN Team Salary Premium (2004 Dollars) 5000

0 10 20 30 40 50 Population Rank 1890

Notes: Team salary premiums are from Model (3) in Table 6. City population ranks obtained from the U.S. Census Bureau at http://www.census.gov/population/www/ documentation/twps0027.html